CPM Homework Help : APCALC Problem 12-24

Multiple Choice: The graph at right shows the growth of a population $P$ of sea lions introduced near a remote island after $t$ years. A reasonable differential equation to model this growth is:

$\frac { d P } { d t } = \frac { 1 } { 800 } P ( 400 - P )$

$\frac { d P } { d t } = \frac { 1 } { 400 } P ( 800 - P )$

$\frac { d P } { d t } = \frac { 1 } { 800 } P$

$\frac { d P } { d t } = \frac { 1 } { 400 } ( 800 - P )$

$\frac { d P } { d t } = \frac { 1 } { 800 } ( 400 - P )$

First quadrant, x axis labeled, t, scaled from 0 to 5, y axis labeled, P, scaled from 0 to 800, continuous curve with the following approximate critical points, starting @ (0, comma 10), passing through (1, comma 25), changing from concave up to concave down @ (2, comma 400), passing through (3, comma 750), leveling off @ (3.5, comma 790).

Hint:

$\frac{dP}{dt} = 0\text{ when }P = 0\text{ and }800.$

Which equation satisfies these conditions?